data(plasma)Practical session 1
NHMRC Clinical Trials Centre, University of Sydney
gillian.heller@sydney.edu.au
Harrell (2002): “Observational studies have suggested that low dietary intake or low plasma concentrations of retinol, beta-carotene, or other carotenoids might be associated with increased risk of developing certain types of cancer … We designed a cross-sectional study to investigate the relationship between personal characteristics and dietary factors, and plasma concentrations of retinol, beta-carotene, and other carotenoids.”
| Variable | Description |
|---|---|
| age | age (years) |
| sex | factor sex (1=male, 2=female) |
| smokstat | factor smoking status (1=never, 2=former, 3=current smoker) |
| bmi | body mass index (weight/(height2)) |
| vituse | factor vitamin use (1=yes, fairly often, 2=yes, not often, 3=no) |
| calories | number of calories consumed per day |
| fat | grams of fat consumed per day |
| fiber | grams of fiber consumed per day |
| alcohol | number of alcoholic drinks consumed per week |
| cholesterol | cholesterol consumed (mg per day) |
| betadiet | dietary beta-carotene consumed (mcg per day) |
| retdiet | dietary retinol consumed (mcg per day) |
| betaplasma | plasma beta-carotene (ng/ml) |
| retplasma | plasma retinol (ng/ml) |
betadiet as the response variable.Clearly one alcohol observation is outlying (203 drinks/week)
In the absence of other information, we exclude it
fitDist(plasma$betadiet, type = "realAll", trace = FALSE)
find_family().. BCCG family
.. .. IC = 5659.624
.. BCCGo family
.. .. IC = 5659.666
.. BCCGuntr family
.. .. error
.. BCPE family
.. .. IC = 5352.343
.. BCPEo family
.. .. IC = 5448.862
.. BCPEuntr family
.. .. error
.. BCT family
.. .. IC = 5335.245
.. BCTo family
.. .. IC = 5335.245
.. BCTuntr family
.. .. error
.. BE family
.. .. error
.. BEo family
.. .. error
.. EGB2 family
.. .. error
.. exGAUS family
.. .. IC = 5335.182
.. EXP family
.. .. IC = 5459.178
.. GA family
.. .. IC = 5340.096
.. GAF family
.. .. IC = 11268.92
.. GB1 family
.. .. error
.. GB2 family
.. .. IC = 5342.274
.. GG family
.. .. IC = 5333.242
.. GIG family
.. .. IC = 5333.237
.. GP family
.. .. IC = 5485.109
.. GT family
.. .. IC = 5423.975
.. GU family
.. .. IC = 5673.845
.. IG family
.. .. IC = 5337.755
.. IGAMMA family
.. .. IC = 5368.155
.. JSU family
.. .. IC = 5338.221
.. JSUo family
.. .. IC = 5349.94
.. LNO family
.. .. error
.. LO family
.. .. IC = 5440.542
.. LOGITNO family
.. .. error
.. LOGNO family
.. .. IC = 5333.183
.. LOGNO2 family
.. .. IC = 5333.183
.. LQNO family
.. .. IC = 5476.541
.. NET family
.. .. error
.. NO family
.. .. IC = 5476.535
.. NO2 family
.. .. IC = 5476.535
.. NOF family
.. .. IC = 5478.535
.. PARETO family
.. .. IC = 6590.391
.. PARETO1 family
.. .. IC = 6590.895
.. PARETO1o family
.. .. error
.. PARETO2 family
.. .. IC = 5485.109
.. PARETO2o family
.. .. IC = 5643.069
.. PE family
.. .. IC = 5487.561
.. PE2 family
.. .. IC = 5446.202
.. RG family
.. .. IC = 5358.632
.. RGE family
.. .. error
.. SEP family
.. .. IC = 5336.446
.. SEP1 family
.. .. IC = 5336.598
.. SEP2 family
.. .. IC = 5336.406
.. SEP3 family
.. .. IC = 5342.212
.. SEP4 family
.. .. IC = 5337.655
.. SHASH family
.. .. IC = 5346.118
.. SHASHo family
.. .. IC = 5340.656
.. SHASHo2 family
.. .. IC = 5339.187
.. SIMPLEX family
.. .. error
.. SN1 family
.. .. IC = 5478.542
.. SN2 family
.. .. IC = 5353.238
.. SST family
.. .. IC = 5337.28
.. ST1 family
.. .. IC = 5336.647
.. ST2 family
.. .. IC = 5336.344
.. ST3 family
.. .. IC = 5338.954
.. ST3C family
.. .. IC = 5338.954
.. ST4 family
.. .. IC = 5385.382
.. ST5 family
.. .. IC = 5354.737
.. TF family
.. .. IC = 5430.886
.. TF2 family
.. .. IC = 5430.985
.. WEI family
.. .. IC = 5360.282
.. WEI2 family
.. .. IC = 5374.119
.. WEI3 family
.. .. IC = 5360.282
GAF PARETO1 PARETO GU BCCGo BCCG PARETO2o PE
11268.918 6590.895 6590.391 5673.845 5659.666 5659.624 5643.069 5487.561
PARETO2 GP SN1 NOF LQNO NO2 NO EXP
5485.109 5485.109 5478.542 5478.536 5476.541 5476.536 5476.536 5459.178
BCPEo PE2 LO TF2 TF GT ST4 WEI2
5448.862 5446.202 5440.542 5430.985 5430.886 5423.975 5385.382 5374.119
IGAMMA WEI WEI3 RG ST5 SN2 BCPE JSUo
5368.155 5360.282 5360.282 5358.631 5354.737 5353.238 5352.343 5349.941
SHASH GB2 SEP3 SHASHo GA SHASHo2 ST3 ST3C
5346.118 5342.274 5342.212 5340.656 5340.096 5339.187 5338.954 5338.954
JSU IG SEP4 SST ST1 SEP1 SEP SEP2
5338.221 5337.755 5337.655 5337.280 5336.647 5336.598 5336.446 5336.406
ST2 BCT BCTo exGAUS GG GIG LOGNO LOGNO2
5336.344 5335.245 5335.245 5335.182 5333.242 5333.237 5333.183 5333.183
Family: c("GIG", "Generalised Inverse Gaussian")
Fitting method: "nlminb"
Call: gamlssML(formula = plasma$betadiet, family = "GIG")
Mu Coefficients:
[1] 7.689
Sigma Coefficients:
[1] -0.2695
Nu Coefficients:
[1] 1.019
Degrees of Freedom for the fit: 3 Residual Deg. of Freedom 311
Global Deviance: 5327.23
AIC: 5333.23
SBC: 5344.48
Family: c("LOGNO2", "Log Normal 2")
Fitting method: "nlminb"
Call: gamlssML(formula = plasma$betadiet, family = "LOGNO2")
Mu Coefficients:
[1] 7.479
Sigma Coefficients:
[1] -0.4119
Degrees of Freedom for the fit: 2 Residual Deg. of Freedom 312
Global Deviance: 5329.18
AIC: 5333.18
SBC: 5340.68
age + fiber + log(cholesterol) for muformula = betadiet ~ age + fiber + log(cholesterol) | 1 | 1 | 1
g <- find_gamlss2(formula, data = plasma, verbose = FALSE,
select = FALSE,
families = available_families(type = "continuous")).. .. IC = 5327.757
.. .. IC = 5337.051
.. .. error
.. .. IC = 5230.775
.. .. IC = 5248.64
.. .. error
.. .. IC = 5218.527
.. .. IC = 5236.207
.. .. error
.. .. error
.. .. error
.. .. IC = 24530.73
.. .. IC = 5279.37
.. .. IC = 5429.382
.. .. IC = 5243.367
.. .. IC = 5245.367
.. .. error
.. .. IC = 5237.519
.. .. IC = 5235.951
.. .. IC = 5239.16
.. .. IC = 5457.182
.. .. IC = 5325.237
.. .. IC = 5602.88
.. .. IC = 5258.039
.. .. IC = 5265.02
.. .. IC = 5281.75
.. .. IC = 5289.245
.. .. error
.. .. IC = 5344.945
.. .. error
.. .. IC = 5235.592
.. .. IC = 5235.592
.. .. IC = 5373.805
.. .. error
.. .. IC = 5395.453
.. .. IC = 5395.453
.. .. IC = 5365.33
.. .. IC = 6595.697
.. .. IC = 6596.203
.. .. error
.. .. IC = 5457.182
.. .. IC = 5649.069
.. .. IC = 5326.55
.. .. IC = 5326.757
.. .. IC = 5289.186
.. .. error
.. .. IC = 5305.991
.. .. IC = 5290.87
.. .. IC = 5297.61
.. .. IC = 5287.474
.. .. IC = 5284.034
.. .. IC = 5282.09
.. .. IC = 5283.886
.. .. IC = 5283.559
.. .. error
.. .. IC = 5397.482
.. .. IC = 5312.301
.. .. IC = 5286.17
.. .. IC = 5290.847
.. .. IC = 5290.699
.. .. IC = 5287.471
.. .. IC = 5287.471
.. .. IC = 5291.873
.. .. IC = 5287.657
.. .. IC = 5323.208
.. .. IC = 5323.556
.. .. IC = 5278.599
.. .. IC = 5281.321
.. .. IC = 5278.599
Call:
gamlss2(formula = formula, data = ..1, family = families[[j]],
... = pairlist(trace = FALSE))
---
Family: BCT
Link function: mu = identity, sigma = log, nu = identity, tau = log
*--------
Coefficients:
Estimate Std. Error t value Pr(>|t|)
mu.(Intercept) -1.656e+03 5.029e+02 -3.293 0.00111 **
mu.age 1.057e+01 3.227e+00 3.275 0.00118 **
mu.fiber 1.272e+02 1.209e+01 10.520 < 2e-16 ***
mu.log(cholesterol) 2.713e+02 9.144e+01 2.967 0.00325 **
sigma.(Intercept) -7.170e-01 6.693e-02 -10.712 < 2e-16 ***
nu.(Intercept) 1.596e-01 1.001e-01 1.595 0.11180
tau.(Intercept) 2.318e+00 5.333e-01 4.346 1.89e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
*--------
n = 314 df = 7 res.df = 307
Deviance = 5204.5267 Null Dev. Red. = 3.38%
AIC = 5218.5267 elapsed = 0.20sec
Options for variable selection are
stepwise selection
LASSO, ridge regression
boosting [not covered]
We use the gamlss function stepGAICAll.A()
I have limited the number of variables considered because of computing time
For each continuous covariate I have included the linear term and a smooth term pb()
Start with model m0
Specify lower and upper scope for all distribution parameters
GAMLSS-RS iteration 1: Global Deviance = 5347.725
GAMLSS-RS iteration 2: Global Deviance = 5328.487
GAMLSS-RS iteration 3: Global Deviance = 5327.318
GAMLSS-RS iteration 4: Global Deviance = 5327.247
GAMLSS-RS iteration 5: Global Deviance = 5327.246
GAMLSS-RS iteration 6: Global Deviance = 5327.246
m.step <- stepGAICAll.A(m0,
scope=list(lower=~1,
upper=~
#age + pb(age) +
factor(sex) + factor(smokstat) + factor(vituse) +
#bmi + pb(bmi) +
#calories + pb(calories) +
fat + pb(fat) +
fiber + pb(fiber) +
#alcohol + pb(alcohol) +
cholesterol + pb(cholesterol) + log(cholesterol)))---------------------------------------------------
Distribution parameter: mu
Start: AIC= 5335.25
betadiet ~ 1
Df AIC
+ pb(fiber) 2.9280 5229.0
+ fiber 1.0000 5242.1
+ pb(cholesterol) 6.2191 5314.3
+ log(cholesterol) 1.0000 5325.9
+ pb(fat) 1.8392 5327.7
+ fat 1.0000 5328.6
+ factor(smokstat) 2.0000 5330.2
+ cholesterol 1.0000 5331.6
+ factor(vituse) 2.0000 5335.2
<none> 5335.2
+ factor(sex) 1.0000 5336.9
Step: AIC= 5229.01
betadiet ~ pb(fiber)
Df AIC
+ pb(cholesterol) 2.74678 5226.2
+ log(cholesterol) 0.92635 5228.8
<none> 5229.0
+ factor(smokstat) 1.94075 5230.0
+ cholesterol 0.96754 5230.6
+ pb(fat) 1.01357 5231.0
+ fat 1.01296 5231.0
+ factor(sex) 0.99938 5231.0
+ factor(vituse) 2.02699 5231.2
Step: AIC= 5226.16
betadiet ~ pb(fiber) + pb(cholesterol)
Df AIC
+ fat 4.36154 5218.9
+ pb(fat) 4.36222 5218.9
+ factor(smokstat) 5.35396 5218.9
+ factor(vituse) 2.40313 5226.1
<none> 5226.2
+ log(cholesterol) -0.80771 5226.7
+ factor(sex) 1.01289 5228.1
Step: AIC= 5218.86
betadiet ~ pb(fiber) + pb(cholesterol) + fat
Df AIC
+ factor(smokstat) 2.49256711 5217.2
<none> 5218.9
+ pb(fat) 0.00067679 5218.9
+ log(cholesterol) 1.21056508 5220.2
+ factor(sex) 1.10724977 5220.4
+ factor(vituse) -0.73403543 5225.3
Step: AIC= 5217.18
betadiet ~ pb(fiber) + pb(cholesterol) + fat + factor(smokstat)
Df AIC
<none> 5217.2
+ pb(fat) 0.00069551 5217.2
+ log(cholesterol) 1.31999672 5218.1
+ factor(sex) 1.10364517 5218.6
+ factor(vituse) 1.75823075 5218.6
---------------------------------------------------
Distribution parameter: sigma
Start: AIC= 5217.18
~1
Df AIC
+ cholesterol 1.55290 5217.1
<none> 5217.2
+ factor(sex) 1.07638 5217.9
+ log(cholesterol) 1.29666 5217.9
+ factor(vituse) 2.19742 5218.6
+ pb(fiber) 1.57421 5218.9
+ fat 0.91267 5218.9
+ pb(fat) 0.91292 5218.9
+ fiber 0.97995 5219.2
+ factor(smokstat) 1.86269 5220.6
+ pb(cholesterol) 31.99645 6529.3
Step: AIC= 5217.08
~cholesterol
Df AIC
<none> 5217.1
+ pb(fiber) 2.18436 5217.9
+ log(cholesterol) 1.37681 5218.1
+ factor(vituse) 2.22721 5218.2
+ factor(sex) 0.99664 5218.3
+ fiber 0.97489 5219.0
+ pb(fat) 0.89050 5219.3
+ fat 0.89152 5219.3
+ factor(smokstat) 2.04224 5219.8
+ pb(cholesterol) 30.44355 6529.3
---------------------------------------------------
Distribution parameter: nu
Start: AIC= 5217.08
~1
Df AIC
<none> 5217.1
+ cholesterol 1.08855 5217.6
+ pb(cholesterol) 1.08863 5217.6
+ log(cholesterol) 1.01471 5217.7
+ factor(sex) 1.09033 5218.3
+ fat 1.09516 5218.4
+ pb(fat) 1.09524 5218.4
+ factor(smokstat) 1.24363 5218.9
+ fiber 0.74450 5219.1
+ pb(fiber) 0.74461 5219.1
+ factor(vituse) 1.97364 5220.0
---------------------------------------------------
Distribution parameter: tau
Start: AIC= 5217.08
~1
Df AIC
<none> 5217.1
+ fiber 0.88883 5217.6
+ pb(fiber) 0.88883 5217.6
+ log(cholesterol) 1.06620 5218.9
+ factor(sex) 0.92675 5218.9
+ fat 0.94527 5219.2
+ pb(fat) 0.94527 5219.2
+ cholesterol 0.94538 5219.2
+ pb(cholesterol) 0.94538 5219.2
+ factor(smokstat) 2.02535 5220.9
+ factor(vituse) -2.17993 5226.1
---------------------------------------------------
Distribution parameter: nu
Start: AIC= 5217.08
~1
---------------------------------------------------
Distribution parameter: sigma
Start: AIC= 5217.08
~cholesterol
Df AIC
<none> 5217.1
- cholesterol 1.5529 5217.2
---------------------------------------------------
Distribution parameter: mu
Start: AIC= 5217.08
betadiet ~ pb(fiber) + pb(cholesterol) + fat + factor(smokstat)
Df AIC
<none> 5217.1
- fat 1.6686 5219.4
- factor(smokstat) 2.6010 5219.6
- pb(cholesterol) 7.2076 5233.8
- pb(fiber) 2.9944 5305.1
---------------------------------------------------
******************************************************************
Family: c("BCTo", "Box-Cox-t-orig.")
Call: gamlss(formula = betadiet ~ pb(fiber) + pb(cholesterol) +
fat + factor(smokstat), sigma.formula = ~cholesterol,
family = BCTo, data = plasma, n.cyc = 50, trace = FALSE,
nu.formula = ~1, tau.formula = ~1)
Fitting method: RS()
------------------------------------------------------------------
Mu link function: log
Mu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.6944554 0.0962626 69.544 <2e-16 ***
pb(fiber) 0.0610383 0.0057819 10.557 <2e-16 ***
pb(cholesterol) 0.0007747 0.0003524 2.199 0.0287 *
fat -0.0021934 0.0012383 -1.771 0.0776 .
factor(smokstat)2 0.0880635 0.0644600 1.366 0.1729
factor(smokstat)3 -0.1243547 0.0901867 -1.379 0.1690
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
Sigma link function: log
Sigma Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.6333595 0.0997791 -6.348 8.2e-10 ***
cholesterol -0.0004655 0.0003697 -1.259 0.209
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
Nu link function: identity
Nu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.2209 0.1136 1.945 0.0528 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
Tau link function: log
Tau Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.4203 0.5969 4.055 6.42e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
NOTE: Additive smoothing terms exist in the formulas:
i) Std. Error for smoothers are for the linear effect only.
ii) Std. Error for the linear terms maybe are not accurate.
------------------------------------------------------------------
No. of observations in the fit: 314
Degrees of Freedom for the fit: 18.08183
Residual Deg. of Freedom: 295.9182
at cycle: 12
Global Deviance: 5180.913
AIC: 5217.076
SBC: 5284.872
******************************************************************
We use the gnet() function in the gamlss.lasso package:
m.lasso <-
gamlss(betadiet~gnet(x.vars= names(plasma)[1:10], method = "IC", ICpen="BIC", adaptive=NULL),
sigma.formula =~ gnet(x.vars= names(plasma)[1:10], method = "IC", ICpen="BIC", adaptive=NULL),
nu.formula =~ gnet(x.vars= names(plasma)[1:10], method = "IC", ICpen="BIC", adaptive=NULL),
tau.formula =~ gnet(x.vars= names(plasma)[1:10], method = "IC", ICpen="BIC", adaptive=NULL),
data=plasma, family=BCTo, bf.cyc=1, trace = FALSE)m.lasso.adaptive <-
gamlss(betadiet~gnet(x.vars= names(plasma)[1:10], method = "IC", ICpen="BIC"),
sigma.formula =~ gnet(x.vars= names(plasma)[1:10], method = "IC", ICpen="BIC"),
nu.formula =~ gnet(x.vars= names(plasma)[1:10], method = "IC", ICpen="BIC"),
tau.formula =~ gnet(x.vars= names(plasma)[1:10], method = "IC", ICpen="BIC"),
data=plasma, family=BCTo, bf.cyc=1, trace = FALSE)Models m.lasso and m.lasso.adaptive only contain linear terms.
Add in logs of all continuous covariates:
plasma |>
mutate(logage = log(age),
logbmi = log(bmi),
logcal = log(calories),
logfat = log(fat),
logfiber = log(fiber),
logalc = log(alcohol+0.1),
logchol = log(cholesterol)) -> plasma
m.lasso.adaptive2 <-
gamlss(betadiet~gnet(x.vars= names(plasma)[c(1:10, 15:21)], method = "IC", ICpen="BIC"),
sigma.formula =~ gnet(x.vars= names(plasma)[c(1:10, 15:21)], method = "IC", ICpen="BIC"),
nu.formula =~ gnet(x.vars= names(plasma)[c(1:10, 15:21)], method = "IC", ICpen="BIC"),
tau.formula =~ gnet(x.vars= names(plasma)[c(1:10, 15:21)], method = "IC", ICpen="BIC"),
data=plasma, family=BCTo, bf.cyc=1, trace = FALSE) df AIC
m.step 18.08183 5217.076
m.lasso.adaptive2 5.00000 5228.704
m.lasso.adaptive 5.00000 5243.379
m.lasso 5.00000 5247.051
df BIC
m.step 18.08183 5284.872
m.lasso 5.00000 5265.798
m.lasso.adaptive 5.00000 5262.126
m.lasso.adaptive2 5.00000 5247.451
AIC selects m.step
BIC selects m.lasso.adaptive2
rbind(mu=tail(getSmo(m.lasso.adaptive2, "mu") ,1)[[1]]$beta,
sigma=tail(getSmo(m.lasso.adaptive2, "sigma") ,1)[[1]]$beta,
nu=tail(getSmo(m.lasso.adaptive2, "nu") ,1)[[1]]$beta,
tau=tail(getSmo(m.lasso.adaptive2, "tau") ,1)[[1]]$beta) age sex smokstat bmi vituse calories fat fiber alcohol cholesterol logage
mu 0 0 0 0 0 0 0 0 0 0 0
sigma 0 0 0 0 0 0 0 0 0 0 0
nu 0 0 0 0 0 0 0 0 0 0 0
tau 0 0 0 0 0 0 0 0 0 0 0
logbmi logcal logfat logfiber logalc logchol
mu 0 0 0 0.8186423 0 0
sigma 0 0 0 0.0000000 0 0
nu 0 0 0 0.0000000 0 0
tau 0 0 0 0.0000000 0 0
rbind(mu=tail(getSmo(m.lasso.adaptive, "mu") ,1)[[1]]$beta,
sigma=tail(getSmo(m.lasso.adaptive, "sigma") ,1)[[1]]$beta,
nu=tail(getSmo(m.lasso.adaptive, "nu") ,1)[[1]]$beta,
tau=tail(getSmo(m.lasso.adaptive, "tau") ,1)[[1]]$beta) age sex smokstat bmi vituse calories fat fiber alcohol cholesterol
mu 0 0 0 0 0 0 0 0.05748841 0 0
sigma 0 0 0 0 0 0 0 0.00000000 0 0
nu 0 0 0 0 0 0 0 0.00000000 0 0
tau 0 0 0 0 0 0 0 0.00000000 0 0
rbind(mu=tail(getSmo(m.lasso.adaptive, "mu") ,1)[[1]]$beta,
sigma=tail(getSmo(m.lasso, "sigma") ,1)[[1]]$beta,
nu=tail(getSmo(m.lasso, "nu") ,1)[[1]]$beta,
tau=tail(getSmo(m.lasso, "tau") ,1)[[1]]$beta) age sex smokstat bmi vituse calories fat fiber alcohol cholesterol
mu 0 0 0 0 0 0 0 0.05748841 0 0
sigma 0 0 0 0 0 0 0 0.00000000 0 0
nu 0 0 0 0 0 0 0 0.00000000 0 0
tau 0 0 0 0 0 0 0 0.00000000 0 0
GAMLSS-RS iteration 1: Global Deviance = 5228.146
GAMLSS-RS iteration 2: Global Deviance = 5218.606
GAMLSS-RS iteration 3: Global Deviance = 5218.37
GAMLSS-RS iteration 4: Global Deviance = 5218.33
GAMLSS-RS iteration 5: Global Deviance = 5218.321
GAMLSS-RS iteration 6: Global Deviance = 5218.318
GAMLSS-RS iteration 7: Global Deviance = 5218.318
******************************************************************
Family: c("BCTo", "Box-Cox-t-orig.")
Call: gamlss(formula = betadiet ~ logfiber, family = BCTo,
data = plasma)
Fitting method: RS()
------------------------------------------------------------------
Mu link function: log
Mu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.37324 0.18403 29.20 <2e-16 ***
logfiber 0.86470 0.07384 11.71 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
Sigma link function: log
Sigma Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.66598 0.06218 -10.71 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
Nu link function: identity
Nu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.16413 0.09424 1.742 0.0826 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
Tau link function: log
Tau Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.6357 0.6472 4.072 5.92e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
No. of observations in the fit: 314
Degrees of Freedom for the fit: 5
Residual Deg. of Freedom: 309
at cycle: 7
Global Deviance: 5218.318
AIC: 5228.318
SBC: 5247.065
******************************************************************
The following finds response distribution and selects variables:
f <- betadiet ~ age + s(age) +
sex + smokstat +
bmi + s(bmi) +
vituse +
calories + s(calories) +
fat + s(fat) +
fiber + s(fiber) +
alcohol + s(alcohol) +
cholesterol + s(cholesterol)|.|.|.
m.gamlss2 <- find_gamlss2(f, data=plasma,
families = available_families(type = "continuous"),
select = TRUE)
summary(m.gamlss2)